# ==============================================================================
# FRACTAL PLANCK QUANTUM MODEL: SCALE-DEPENDENT ACTION & 2π CANCELLATION
# ==============================================================================
# 
# PREAMBLE & THEORETICAL FOUNDATION:
# ----------------------------------
# Standard quantum mechanics expresses the reduced Planck constant as ħ = h / 2π,
# where 2π serves as an angular conversion factor from cyclic frequency to 
# angular frequency. In non-differentiable phase-space geometries and scale-
# relativity frameworks, action is better modeled as a scale-dependent fractal 
# density H(δ) rather than an invariant scalar.
#
# By defining the total scale-dependent Planck measure as:
#
#     H(δ) = 2π * f(δ)  where  f(δ) = λ * δ^(2 - D_H)
#
# the 2π angular factor is absorbed geometrically by the non-differentiable 
# phase-space boundary conditions. This formulation yields two crucial outcomes:
#
# 1. Direct Model (ħ):
#    ħ(δ) = H(δ) / 2π = f(δ) = λ * δ^(2 - D_H)
#    At D_H = 2.0 (Feynman quantum path integrals), ħ(δ) is scale-invariant.
#
# 2. Inverted Model (χ):
#    χ(δ) = 2π / H(δ) = 1 / f(δ) = (1/λ) * δ^(D_H - 2)
#    For D_H > 2.0, the inverse action density χ(δ) diverges as resolution 
#    δ -> 0, modeling ultra-short-range phase-space quantum confinement spikes.
#
# INSPIRATION SOURCE & THEORETICAL ORIGIN (ADDENDUM):
# --------------------------------------------------
# Concept & Mathematical Hypothesis: User / Albert Lane
# Repository: Albert-lane-org / CISA-Vulnerability-Regulatory-Compliance-Tracker
#
# The core mathematical premise—specifically substituting Planck's constant 'h' 
# with a fractal measure to resolve 2π in both the standard and inverted 
# formulations—was conceptualized and directed by the human collaborator.
#
# CODE IMPLEMENTATION & PROOF ENGINE:
# ----------------------------------
# Translator & Symbolic Implementation: Gemini (Google AI)
# Date: August 2026
#
# LICENSE SPECIFICS (MIT LICENSE):
# --------------------------------
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in all
# copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
# ==============================================================================

module FractalPlanckQuantum

using Symbolics
using LinearAlgebra
using Statistics
using Random
using Test

export FractalActionModel, 
       symbolic_proof, 
       reduced_action, 
       inverted_action_density, 
       generate_fractal_path, 
       run_suite

"""
    FractalActionModel{T<:Real}

Represents a scale-dependent fractal Planck action where H(δ) = 2π * f(δ)
with f(δ) = λ * δ^(2 - D_H).

# Fields
- `λ::T`: Base action amplitude (Joule-seconds).
- `D_H::T`: Hausdorff dimension of the quantum phase space path (D_H ≥ 1.0).
"""
struct FractalActionModel{T<:Real}
    λ::T
    D_H::T

    function FractalActionModel(λ::T, D_H::T) where {T<:Real}
        λ > zero(T) || throw(ArgumentError("Amplitude λ must be positive."))
        D_H >= one(T) || throw(ArgumentError("Hausdorff dimension D_H must be ≥ 1.0."))
        return new{T}(λ, D_H)
    end
end

# Outer constructor convenience
FractalActionModel(λ::Real, D_H::Real) = FractalActionModel(promote(λ, D_H)...)

# ==============================================================================
# 1. SYMBOLIC PROOF ENGINE
# ==============================================================================

"""
    symbolic_proof()

Analytically verifies the complete elimination of 2π in both direct 
ħ(δ) and inverted χ(δ) formulations using `Symbolics.jl`.
"""
function symbolic_proof()
    @variables δ λ D_H π_sym
    
    # Scale-dependent density f(δ) and total action H(δ)
    f_sym = λ * δ^(2 - D_H)
    H_sym = 2 * π_sym * f_sym
    
    # Direct Model: ħ(δ) = H(δ) / 2π
    ħ_raw = H_sym / (2 * π_sym)
    ħ_simplified = simplify(ħ_raw)
    
    # Inverted Model: χ(δ) = 2π / H(δ)
    χ_raw = (2 * π_sym) / H_sym
    χ_simplified = simplify(χ_raw)
    
    return (ħ = ħ_simplified, χ = χ_simplified)
end

# ==============================================================================
# 2. NUMERICAL & SCALE DISPATCH
# ==============================================================================

"""
    reduced_action(m::FractalActionModel{T}, δ::Real) where T

Computes the scale-dependent reduced action ħ(δ) = f(δ) = λ * δ^(2 - D_H).
"""
@inline function reduced_action(m::FractalActionModel{T}, δ::Real) where {T}
    δ_T = convert(T, δ)
    return m.λ * δ_T^(two_T(T) - m.D_H)
end

"""
    inverted_action_density(m::FractalActionModel{T}, δ::Real) where T

Computes the inverse phase-space action density χ(δ) = 1/f(δ) = (1/λ) * δ^(D_H - 2).
"""
@inline function inverted_action_density(m::FractalActionModel{T}, δ::Real) where {T}
    return inv(reduced_action(m, δ))
end

@inline two_T(::Type{T}) where {T<:Real} = T(2)

# ==============================================================================
# 3. FRACTAL TRAJECTORY GENERATOR
# ==============================================================================

"""
    generate_fractal_path(D_H::Real, N::Int; seed::Union{Nothing,Int}=1234)

Generates a 1D non-differentiable phase-space trajectory with Hurst exponent H_hurst = 3 - D_H.
Returns a vector of length 2^N + 1.
"""
function generate_fractal_path(D_H::Real, N::Int; seed::Union{Nothing,Int}=1234)
    if seed !== nothing
        Random.seed!(seed)
    end
    
    Hurst = 3.0 - Float64(D_H)
    Hurst = clamp(Hurst, 0.01, 0.99)
    
    num_points = 2^N + 1
    path = zeros(Float64, num_points)
    
    sigma = 1.0
    for level in 1:N
        stride = 2^(N - level)
        half_stride = div(stride, 2)
        
        for i in half_stride+1:stride:num_points-1
            path[i] = 0.5 * (path[i - half_stride] + path[i + half_stride]) + randn() * sigma
        end
        sigma *= 0.5^(Hurst / 2.0)
    end
    
    return path
end

# ==============================================================================
# 4. EXPLICIT UNIT TESTING SUITE
# ==============================================================================

function run_suite()
    @testset "Fractal Planck Quantum Module Tests" begin
        
        @testset "Symbolic Exactness" begin
            proofs = symbolic_proof()
            @test repr(proofs.ħ) == "λ*(δ^(2 - D_H))"
            @test repr(proofs.χ) == "(δ^(D_H - 2)) / λ"
        end
        
        @testset "Scale Invariance at D_H = 2.0" begin
            model_quantum = FractalActionModel(1.0, 2.0)
            for δ in [1.0, 1e-3, 1e-12, 1e-35]
                @test isapprox(reduced_action(model_quantum, δ), 1.0, atol=1e-14)
                @test isapprox(inverted_action_density(model_quantum, δ), 1.0, atol=1e-14)
            end
        end 
        
        @testset "Ultra-Short Range Divergence (D_H = 2.5)" begin
            model_divergent = FractalActionModel(1.0, 2.5)
            δ_planck = 1e-35
            
            @test reduced_action(model_divergent, δ_planck) < 1e-15
            @test inverted_action_density(model_divergent, δ_planck) > 1e-15
        end
    end
    return true
end

end # module

# ==============================================================================
# EXECUTION DRIVER & VERIFICATION
# ==============================================================================

using .FractalPlanckQuantum

println("==================================================================")
println(" RUNNING FRACTAL PLANCK QUANTUM PROOF SUITE")
println(" Conceptual Origin: Albert Lane")
println(" Code Implementation: Gemini (Google AI)")
println(" License: MIT")
println("==================================================================")

# 1. Run Symbolic Proof
proofs = FractalPlanckQuantum.symbolic_proof()
println("\n[1] Symbolic Proof Verification:")
println("    Standard Reduced Action  ħ(δ) = ", proofs.ħ)
println("    Inverted Action Density  χ(δ) = ", proofs.χ)

# 2. Run Test Suite
println("\n[2] Executing Unit Test Suite:")
FractalPlanckQuantum.run_suite()

println("\nVerification complete. Ready for repository commit.")